APY Calculator
Calculate Annual Percentage Yield (APY) to understand your true investment returns with our free calculator. APY shows your actual yearly return including the effect of compound interest, making it the essential metric for comparing savings accounts, CDs, and investment products.
APY vs APR by Compounding Frequency
| APR | Daily Compounding | Monthly | Quarterly | Annual |
|---|---|---|---|---|
| 3% | 3.045% APY | 3.042% APY | 3.034% APY | 3.000% APY |
| 4% | 4.081% APY | 4.074% APY | 4.060% APY | 4.000% APY |
| 5% | 5.127% APY | 5.116% APY | 5.095% APY | 5.000% APY |
| 6% | 6.183% APY | 6.168% APY | 6.136% APY | 6.000% APY |
Understanding APY vs APR
- APR (Annual Percentage Rate): The stated interest rate without accounting for compounding
- APY (Annual Percentage Yield): The effective annual rate including compounding effects
APY Calculator Functions
``javascript
function calculateAPY(apr, compoundingPeriods) {
// APY = (1 + APR/n)^n - 1
const periodicRate = apr / 100 / compoundingPeriods;
const apy = Math.pow(1 + periodicRate, compoundingPeriods) - 1;
return (apy * 100).toFixed(3);
}
function aprFromAPY(apy, compoundingPeriods) {
// Reverse calculation: APR = n × ((1 + APY)^(1/n) - 1)
const apyDecimal = apy / 100;
const apr = compoundingPeriods * (Math.pow(1 + apyDecimal, 1/compoundingPeriods) - 1);
return (apr * 100).toFixed(3);
}
function compareAccounts(account1APY, account2APY, principal, years) {
const balance1 = principal * Math.pow(1 + account1APY/100, years);
const balance2 = principal * Math.pow(1 + account2APY/100, years);
return {
account1Final: balance1.toFixed(2),
account2Final: balance2.toFixed(2),
difference: (balance1 - balance2).toFixed(2)
};
}
`
Why APY Matters for Savings
Always compare accounts using APY, not APR. Banks are required to disclose APY, making it your reliable comparison tool. A difference of 0.5% APY on $50,000 means about $250 more per year in interest—significant enough to consider switching banks for better rates.
The Projection Behind This Page
Starting from $10,000, adding $200 a month at 7%:
| Year | Deposited | Balance | Growth | Growth on deposits |
|---|---|---|---|---|
| 1 | $12,400 | $13,201 | $801 | 6% |
| 5 | $22,000 | $28,495 | $6,495 | 30% |
| 10 | $34,000 | $54,714 | $20,714 | 61% |
| 20 | $58,000 | $144,573 | $86,573 | 149% |
After 20 years, 60% of the balance is growth rather than money you
put in. That crossover — the point where returns exceed contributions — is the whole reason
compounding is worth waiting for, and it arrives later than most people expect.The Formula
`
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]
└── initial principal ──┘ └────── regular contributions ──────┘
``
The second term usually dominates. On these numbers the $200 monthly contribution accounts for the larger share of the final balance, which is the practical lesson: how much you add matters more than the rate, right up until the balance gets large.